57.4.17 problem 7

Internal problem ID [14341]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:31:53 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=2 t x^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.103 (sec). Leaf size: 13

ode:=diff(x(t),t) = 2*t*x(t)^2; 
ic:=[x(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -\frac {1}{t^{2}-1} \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 14

ode=D[x[t],t]==2*t*x[t]^2; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {1}{1-t^2} \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-2*t*x(t)**2 + Derivative(x(t), t),0) 
ics = {x(0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - \frac {1}{t^{2} - 1} \]